Question

3x+4y-6z=-60
7x-5y+z=-37
2x+3y-z=-29

Answer 1

Solve by substitution/elimination.

From the third equation: 2x+3y−z = −29 ⇒ z = 29 + 2x + 3y.

Sub into the other two:
7x − 5y + (29 + 2x + 3y) = −37 ⇒ 9x − 2y = −66.
3x + 4y − 6(29 + 2x + 3y) = −60 ⇒ 9x + 14y = −114.

Subtract the first from the second: 16y = −48 ⇒ y = −3.
Then 9x − 2(−3) = −66 ⇒ 9x + 6 = −66 ⇒ x = −8.
Finally z = 29 + 2(−8) + 3(−3) = 4.

Solution: x = −8, y = −3, z = 4.